Type of Credit: Elective
Credit(s)
Number of Students
This course covers various topics in probability and large sample theory, including Fubini's theorem, integration to the limit, central limit theorem, conditional probability and conditional expectation, Brownian motion, and some selected topics.
能力項目說明
Upon successful completiong students will understand the core concepts of probability theory.
| 教學週次Course Week | 彈性補充教學週次Flexible Supplemental Instruction Week | 彈性補充教學類別Flexible Supplemental Instruction Type |
|---|---|---|
「周次」 「課程主題」 「課程內容與指定閱讀」 「教學活動與作業」 (暫定）
1 Integration and Integration to the limit book/handouts lecture
2 Fubini's theorem and Integration by parts book/handouts lecture/homework
3 Stein's lemma and James-Stein's estimator book/handouts lecture
4 Woodroofe-Stein's identity and its applications book/handouts lecture/homework
5 Central limit theorem, Edgeworth expansions book/handouts lecture
6 Bayesian central limit theorem book/handouts lecture
7 Exam I
8 Lindeberg condition, CLT for independent variables book/handouts lecture/homework
9 Martingale central limit theorem book/handouts lecture
10 Conditional probability and conditional expectation book/handouts
11 Conditional probability and conditional expectation book/handouts lecture/homework
12 Jensen's inequality and applications book/handouts lecture
13 Brownian motion and applications book/handouts lecture/homework
14 Exam II
15 Selected topics handouts lecture
16 student presentation handouts/papers student presentation
17 Course-related online learning online materials online learning
18 Course-related online learning online materials online learning
1. homework 25%
2. exams (I and II) 50%
4. presentation 25%
Probability and Measure, (3rd ed. Wiley) by Patrick Billingsley
Stochastic Processes, (2nd ed. Wiley) by Sheldon Ross